Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 2ecoptocl | Unicode version |
Description: Implicit substitution of classes for equivalence classes of ordered pairs. (Contributed by NM, 23-Jul-1995.) |
Ref | Expression |
---|---|
2ecoptocl.1 | |
2ecoptocl.2 | |
2ecoptocl.3 | |
2ecoptocl.4 |
Ref | Expression |
---|---|
2ecoptocl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2ecoptocl.1 | . . 3 | |
2 | 2ecoptocl.3 | . . . 4 | |
3 | 2 | imbi2d 229 | . . 3 |
4 | 2ecoptocl.2 | . . . . . 6 | |
5 | 4 | imbi2d 229 | . . . . 5 |
6 | 2ecoptocl.4 | . . . . . 6 | |
7 | 6 | ex 114 | . . . . 5 |
8 | 1, 5, 7 | ecoptocl 6509 | . . . 4 |
9 | 8 | com12 30 | . . 3 |
10 | 1, 3, 9 | ecoptocl 6509 | . 2 |
11 | 10 | impcom 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cop 3525 cxp 4532 cec 6420 cqs 6421 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-xp 4540 df-cnv 4542 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-ec 6424 df-qs 6428 |
This theorem is referenced by: 3ecoptocl 6511 ecovcom 6529 ecovicom 6530 addclnq 7176 mulclnq 7177 nqtri3or 7197 ltexnqq 7209 addclnq0 7252 mulclnq0 7253 distrnq0 7260 mulcomnq0 7261 addassnq0 7263 addclsr 7554 mulclsr 7555 mulgt0sr 7579 aptisr 7580 |
Copyright terms: Public domain | W3C validator |